Question

56. A thin, uniform rod of mass M and length L is
rotated with constant angular speed o as shown in
figure. Tension in the rod at position A

Answer 1

Answer:

T(x)−T(x+dx)=

L

M

w

2

xdx (by taylors series formula)

−dT=

L

M

w

2

xdx (formulating the differential equation)

∫

T

x

T

0

dT=−∫

x

0

L

M

w

2

xdx

T

(x)

−T

(0)

=−[

2L

M

w

2

x

2

]

0

x

Now,whenx=L,T(L)=0

Thus,T(0)=

2L

M

w

2

L

2

Hence,T(x)=

2L

M

w

2

(L

2

−x

2

)

∴T(

2

L

)=

2L

M

w

2

(L

2

−

4

L

2

)

Hence,T(

2

L

)=

8

3

MLw

2